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A240868
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Number of partitions of n into distinct parts of which the number of even parts is not a part and the number of odd parts is not a part.
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7
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0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 7, 8, 10, 10, 16, 15, 23, 19, 32, 27, 44, 36, 60, 50, 80, 67, 103, 92, 137, 124, 174, 167, 224, 221, 284, 292, 362, 382, 453, 497, 574, 641, 715, 821, 897, 1046, 1117, 1323, 1396, 1664, 1729, 2082, 2151, 2591, 2660, 3213
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OFFSET
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0,5
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LINKS
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EXAMPLE
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a(9) counts these 4 partitions: 9, 72, 63, 54.
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MATHEMATICA
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z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
t1 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240862 *)
t2 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240863, *)
t3 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240864 *)
t4 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240865 *)
t5 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240866 *)
t6 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240867 *)
t7 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240868 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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